A paradox is a statement or group of statements that leads to a contradiction or a situation which defies intuition. The term is also used for an apparent contradiction that actually expresses a non-dual truth.

Definition of paradox can be complicated. It can be roughly simplified as “two facts contradicting each other. Which one will you choose if a truth contradicts another truth ? Let’s see some examples, starting from simple ones.

Liar's paradox

This is the simplest of paradoxes and can be created by uttering a single phrase: “I always lie”. If he is always lying than what he just said can’t be true, if it isn’t true than he doesn’t lie and if he didn’t lie he is a liar... and this goes on forever creating an endless loop. There are many variations of the liar paradox. Imagine a card. On one side is written “The sentence on the other side of this card is true” and on the back side is written “the sentence on the other side of this card is false”. Or think of two men called A and B. A says “B always says the truth” and B says “A is a liar” two paradoxes are practically same. The second statement overturns the meaning of the first one which overturns the meaning of second one and creates an endless loop.

Now we know what a paradox is. Let’s see some funny ones.

Some of the best Paradoxes are “Zeno’s paradoxes”. He was a Greek of southern Italy who made up paradoxes which contradicted our 5 senses and commonly accepted truths.

Achilles and the tortoise

In a race, the quickest runner can never overtake the slowest, since the pursuer must first reach the point whence the pursued started, so that the slower must always hold a lead.

In the paradox of Achilles and the tortoise, Achilles is in a footrace with the tortoise. Achilles allows the tortoise a head start of 100 meters. If we suppose that each racer starts running at some constant speed (one very fast and one very slow), then after some finite time, Achilles will have run 100 meters, bringing him to the tortoise's starting point. During this time, the tortoise has run a much shorter distance, say, 10 meters. It will then take Achilles some further time to run that distance, by which time the tortoise will have advanced farther; and then more time still to reach this third point, while the tortoise moves ahead. Thus, whenever Achilles reaches somewhere the tortoise has been, he still has farther to go. Therefore, because there are an infinite number of points Achilles must reach where the tortoise has already been, he can never overtake the tortoise. Of course, simple experience tells us that Achilles will be able to overtake the tortoise, which is why this is a paradox

The dichotomy paradox

That which is in locomotion must arrive at the half-way stage before it arrives at the goal.

SupposeHomerwants to catch a stationary bus. Before he can get there, he must get halfway there. Before he can get halfway there, he must get a quarter of the way there. Before travelling a fourth, he must travel one-eighth; before an eighth, one-sixteenth; and so on.

The act requires infinite number of actions which Zeno maintains is an impossibility. This paradox presents a second problem. Since every finite distance requires an infinite number of actions even the shortest imaginable distance requires infinite number of actions. Therefore nothing can move let alone arrive at some point.

The arrow paradox

If everything when it occupies an equal space is at rest, and if that which is in locomotion is always occupying such a space at any moment, the flying arrow is therefore motionless.

In the arrow paradox, Zeno states that for motion to be occurring, an object must change the position which it occupies. He gives an example of an arrow in flight. He states that in any one instant of time, for the arrow to be moving it must either move to where it is, or it must move to where it is not. However, it cannot move to where it is not, because this is a single instant, and it cannot move to where it is because it is already there. In other words, in any instant of time there is no motion occurring, because an instant is a snapshot. Therefore, if it cannot move in a single instant it cannot move in any instant, making any motion impossible.

More paradoxes

As you see words can be really confusing sometimes. How can someone state the contrary of the truth and can still be saying something so truthful you can’t deny?

Let’s see one more example like this. Actually it’s a question. Something closer home:

A Saturday afternoon at the end of the last class, a Professor tells the students that, there will be a quiz next week but he doesn’t say which day and adds “If you can guess correctly which day the quiz will be held you will all pass. But if you are wrong you all fail”

What would you do if you were a student? In which day you would do the quiz if you were the PGP office?

First thing that comes in to mind is that teacher can’t do the quiz on Saturday. Since it’s the last day of the week all the students will now that the test will be held that day hence there is no days left. Let’s think about Friday. Since students know that teacher can’t do the test on Saturday they can neglect it therefore if the teacher waits till Friday they will know that the test will be held on that day. With this logic we can continue until we reach Monday and come to the conclusion that teacher can’t do the exam! But we know that it isn’t the truth. We have another paradox.

These paradoxes are complex and made up. But we also see paradoxical sentences in daily life such as “Nobody goes to that club, it’s too crowded”

Hollywood paradoxes

One of the sources of most intriguing paradoxes is time travel and there are many examples of Hollywood movies. Let’s take “Back to the Future” even though it’s a cult- favorite, logically it’s a mess. Marty and professor go back in time and by mistake they prevent Marty’s parent from falling in love, therefore jeopardizing Marty’s existence. He slowly starts to fade away to nothingness. This is called the grandfather paradox. The paradox is this: suppose a man travelled back in time and killed his biological grandfather before the latter met the traveller's grandmother. As a result, one of the traveller's parents (and by extension the traveller himself) would never have been conceived. This would imply that he could not have travelled back in time after all, which means the grandfather would still be alive, and the traveller would have been conceived allowing him to travel back in time and kill his grandfather. Thus each possibility seems to imply its own negation. So if Marty somehow prevents his parents from conceiving him he would have never existed, therefore could never go back in time ad infitum.

We see the reverse of this paradox in terminator series. John Connor sends one of his soldiers back in time to protect his mother (machines are trying to kill his mother to eradicate john). And that soldier has sex with John's mother, leading to his existence. So John created his own existence. Can something be its own reason? John sending his soldier back in time to be his father means that if everything goes normally John would have never existed. So how can an inexistent man decide to send his father back in time to be the reason of his own existence? well... simply put, he can’t. These paradoxes actually tell us that going back in time is absolutely impossible. Only way around it is the theory of parallel universes. Each time you go back in time and step on a bug (butterfly effect) you create a parallel universe in which the bug is dead. On the other universe the same bug lives on, bites some electrical cords in a nearby house causes a short circuit, somebody panics and falls down, hit his head and that somebody was supposed to be the father of the man who would discover cold fusion .